{"paper":{"title":"Strange shadows of $\\ell_p$-balls","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.PR","authors_text":"Mathias Sonnleitner, Zakhar Kabluchko","submitted_at":"2024-12-23T11:00:34Z","abstract_excerpt":"We prove a large deviations principle for orthogonal projections of the unit ball $\\mathbb{B}_p^n$ of $\\ell_p^n$ onto a random $k$-dimensional linear subspace of $\\mathbb{R}^n$ as $n\\to\\infty$ in the case $2<p\\le \\infty$ and for the intersection of $\\mathbb{B}_p^n$ with a random $k$-dimensional subspace in the case $1\\le p <2$. The corresponding rate function is finite only on $L_q$-zonoids and their duals, respectively, and given in terms of the maximum entropy over suitable measures generating the $L_q$-zonoid, where $\\frac{1}{p}+\\frac{1}{q}=1$. In particular, we obtain that the renormalized"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.17475","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.17475/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}